^ 



the elementary Relations of Figure and Forces. 197 



tion ; or, to speak in plainer terms, he has to ascertain some fa^t 

 or property containing the complete definition of tlie rela- 

 tions he has recognised : and the analyst has to search for cir- 

 cumstances which may lead him to the determination of if. In 

 the former case the definition must be obtained in the only 

 manner in which the character of the visible world can be 

 made known to intellect, viz. by experiment : and since f is 

 merely the symbolic representation of a figure, nothing de- 

 finitive of it can be primarily obtained, excepting from that 

 figure, and consequently fiom experiment also. From the 

 circumstance that the equation determining <p must be one 

 with six values, the analj'st knows that at least three of the 

 quantities included in <^ must exist co-indeterminately — super- 

 position informs him that ordy three can exist in such a state : 

 and this, in union with his experimental knowledge of the 

 abstract quantities a, b, c, A, B, C, is sufficient to guide him in 

 his varied transformations and final evaluation of 'p. Such 

 then are the two methods, agreeing most scrupulously in the 

 minutest circumstance affecting the principles on which they 

 rest, and differing* only in the different artifices by which 

 they particularize, transform, and combine the experimental 

 facts. If the prejudice to which I have alluded had not ope- 

 rated more forcibly than any prejudice should operate within 

 the cold and calm regions of science, this nice philosophical 

 agreement had never been overlooked, and the invidious and 

 unfounded distinction never drawn. 



In reverting to the extract from Leslie's Geometry, I give 

 immediate assent to the remark respecting the famous analyses 

 of the laws of motion by Euler, D'Alembert, &c. They are 

 essentially unphilosophical and fallacious. But I am not dis- 

 posed either to extend the same agreement to the remark re- 

 lative to the composition of forces, or to recognise the p/iiloso- 

 phical accuracy of the investigation which the learned Pro- 

 fessor has himself given of it. It is remarked somewhere by 

 D'Alembert, that the more abstract an investigation is made, 

 the more perspicuous and satisfactory does it become. How- 

 ever paradoxical this may appear, it is nevertheless true. The 

 nearer that any investigation approaches to an abstracted in- 



• The only distinction that can be drawn a priori betwixt the two me- 

 thods respects the comparative facility of the analytical. The geometer 

 as he proceeds has to invent his logic or his methods of transformation ; 

 whereas the analyst has merely to apply the same treatment which he has 

 been accustomed to give to similar cases. Perha[)S too the course of par- 

 ticularizing a more general functional equation than I adopted above would 

 lead to a scientific arrangement of the objects of geometry. The present 

 arrangement resembles the artificial classiiications of natural history. 



tellectual 



